SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 65 of 100

Marks: +1, -0

A right circular cylinder having diameter 21 cm and height 38 cm is full of ice cream. The ice cream is to be filled in cones of height 12 cm and diameter 7 cm having a hemispherical shape on the top. The number of such cones to be filled with ice cream is

Validate

Solution:

(1) Total volume of ice-cream

=\π r^{2} h

=\π( {21}/{2} )^{2} ×38 {\cu} . {\cm}

= {8379 \π}/{2}

cu. cm.
For a cone of ice-cream,
Volume of cone

= {1}/{3} \π×( {7}/{2} )^{2}× 12 {\cu} . {\cm}

∴ Volume of hemi–sphere

= {2}/{3} \π( {7}/{2} )^{3}

cu. cm.
Total volume of cone–shaped ice cream

= {\π}/{3}\ ( {49}/{4}×12+ {343}/{4} )

cu. cm.

= {\π}/{3} (147+ {343}/{4} )

cu. cm.

= {\π}/{3} ( {588+343}/{4} )

cu. cm.

= {\π}/{3}×{931}/{4}

cu. cm.

∴

Number of cones

= {8379 \π}/{2}×{3 ×4}/{\π× 931}=54

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